Physics 1

A small block of mass MB= 0.50 kg is placed on a long slab of mass MS= 3.0 kg as shown below. Initially, the slab is at rest and the block has a speed v0of 4.0 m/s to the right. The coefficient of kinetic friction between the block and slab is 0.20, and there is no friction between the slab and the horizontal surface on which it moves.

A 5 kg lawn mower is being pushed with an applied force of Fa= 20 N, at an angle of θ. There is a frictional force, F$_f$ opposing the movement of the lawn mower of 10 N. Given that the lawn mower is accelerating at 0.4 m/s$^2$:

A block of mass mis pulled along a rough horizontal surface by a constant applied force of magnitude F1that acts at an angle θto the horizontal, as indicated below. The acceleration of the block is a1. Express all algebraic answers in terms of m, F1, θ, a1, and fundamental constants.

A rubber ball of mass m is dropped from a cliff. As the ball falls, it is subject to air drag (a resistive force caused by the air). The drag force on the ball has a magnitude bv2, where bis a constant drag coefficient and v is the instantaneous speed of the ball. The drag coefficient bis directly proportional to the cross-sectional area of the ball and the density of the air and does not depend on the mass of the ball. As the ball falls, its speed approaches a constant value called the terminal speed.

Draw and label all the forces on the ball at some instant before it reaches terminal speed.

State whether the magnitude of the acceleration of the ball of mass m increases, decreases, or remains the same as the ball approaches terminal speed. Explain.

Write, but do NOT solve, a differential equation for the instantaneous speed vof the ball in terms of time t, the given quantities, and fundamental constants.

Determine the terminal speed vtin terms of the given quantities and fundamental constants.

Determine the energy dissipated by the drag force during the fall if the ball is released at height hand reaches its terminal speed before hitting the ground, in terms of the given quantities and fundamental constants. (this question requires knowledge of potential and kinetic energy, often not introduced until later in a physics course)

A student is swinging a mass, m = 2.0 kg, in a uniform vertical circle of radius R = 2.5 m. The period of the rotation is 2.8 seconds. Draw a free body diagram for the mass at the top of the circle and find the tension of the string (ignore friction and the mass of the string.) Repeat for the mass at the bottom of the rotation.

A car is driving in a circle on an embanked road as shown below. Draw a free body diagram for the car, ignoring friction.

Given that the radius of orbit for the moon is 3.8 x 10$^8$ m, the period of the moon's orbit is 2.36 x 10$^6$ s, and the radius of the earth is 6.38 x 10$^6$ m; Find the altitude of a geostationary satellite.(hint: use Kepler's third law.)

Find the period of a satellite at an altitude of 200 km.

R$_E$ = 6.38 x 10$^6$ m

M$_E$ = 5.98 x 10$^{24}$ kg

G = 6.67 x 10$^{-11}$ $\frac{Nm^2}{kg^2}$

A 20 kg student is about to go down a slide. There is a 3 N frictional force opposing his movement. Assume his velocity at the top of the slide is 0 m/s. Find his velocity at the bottom of the slide.

A marble, m, of mass 100 g is placed onto a platform attached to a spring. The weight of the marble compresses the spring 2 cm, as shown below. A force is then applied to the platform to compress the spring an additional 3 cm. When the force is taken away, the spring decompresses and launches the marble upward. What is the maximum height the marble obtains above the unstretched spring (the spring with no mass on it).

In an experiment to determine the spring constant of an elastic cord of length 0.60 m, a student hangs the cord from a rod and then attaches a variety of weights to the cord. For each weight, the student allows the weight to hang in equilibrium and then measures the entire length of the cord. The data are recorded in the table below:

iii. Calculate the maximum speed of the object.

A small sphere is moving at a constant speed in a vertical circle. Which of the following quantities is changing?

i. kinetic energy    ii. potential energy    iii. momentum

i and ii only

i and iii only

i and ii only

ii only

iii only

ii and iii only

In the situation above, after block 1 comes to rest, the force exerted on the rope must be equal in magnitude to

A. Zero

B. the frictional force on block 1

C. the vector sum of the force on block 1 due to the friction and tension in the spring

D. the sum of the weights of the two blocks

E. Shiang doesn't care, he just wants to sleep

F. the difference in the weights of the two blocks

A solid brass block of mass m slides along a frictionless track when released from rest along the straight section. The circular loop has a radius R.

B. Assume the block is released at height h = 6.0 R, what are the magnitude and direction of the horizontal force competent acting on the block at point Q?

The mass shown below is blown apart into three pieces. Find the direction and velocity of the pink piece.

In a laboratory experiment, you wish to determine the initial speed of a dart just after it leaves a dart gun. The dart of mass $m$ is fired with the gun very close to a wooden block of mass $M_0$ which hangs from a cord of length $l$ and negligible mass as shown below. Assume the size of the block is negligible compared to $l$ and the dart is moving horizontally when it hits the left side of the block at its center and becomes embedded in it. The block swings up to a maximum angle $\theta_{max}$ from the vertical. Express your answer to the following in terms of $m$ , $M_0$ , $l$ , $\theta_{max}$ , and $g$ .

C. The dart is now shot into a block of wood that is fixed in place. The block exerts a force F on the dart that is proportional to the dart's velocity v and in the opposite direction, that is F = -bv, where b is a constant. Derive an expression for the distance L that the dart penetrates into the block in terms of m, $v_0$ , and b.

The wheel shown below has eight equally spaced spokes and a radius of 30 cm. It is mounted on a fixed axle and is spinning at 2.5 rev/sec. You want to shoot a 20 cm long arrow without hitting any of the spokes. Assume the arrow and the spokes are very thin.

B. Does it matter where between the axle and the rim of the wheel you aim? If so what is the best location?

A massless string is wrapped around a disk of rotational inertia I = $\frac{1}{2} m R^2$ . The disk falls and spins as it falls, unraveling the rope. Determine the tension in the string and the acceleration of the disk.

A solid brass sphere of mass m and radius r << R rolls along a track when released from rest along the straight section. The circular loop has a radius R.

B. Assume the sphere is released at height h = 6.0 R, what are the magnitude and direction of the horizontal force competent acting on the sphere at point Q?

A pulley of radius R1and rotational inertia I1is mounted on an axle with negligible friction. A light cord passing over the pulley has two blocks of mass mattached to either end, as shown below. Assume that the cord does not slip on the pulley. Determine the answers to parts (A) and (B) in terms of m, R1, I1, and fundamental constants.