Physics 1

Two sleds are attached by a rope and are being pulled by an applied force, Fa= 100 N. There is 40 N of frictional force opposing movement on each sled. Draw a free body diagram to help find:

Determine the acceleration of the system if M = 5 kg and m = 10 kg and $\theta$ = 30 degrees. There is also a coefficient of friction, $\mu$ = 0.2. Use a free body diagram to determine the tension in the rope and the acceleration of the system.

The large block M is 20 kg, and the smaller block, m, is 1 kg. The coefficient of kinetic friction is 0.2. Determine the acceleration of the system and the tension in the cords. The angle of the inclined plane is 60 degrees to the horizontal. Also draw a free body diagram for both blocks.

Block M = 5 kg and block m = 6 kg. The coefficient of friction is 0.5. Determine the acceleration of the system and the tension in the cord. The angle of the inclined plane is 20 degrees to the horizontal. Draw a free body diagram for the 5 kg block to help find the answer.

Determine the acceleration of the system if m$_1$ = 3 kg and m$_2$ = 8 kg and the pulley has no mass. Determine the tension in the rope as well.

Determine the acceleration of the system if m$_1$ = 5 kg and m$_2$ = 10 kg and m$_3$. Determine the tensions T, T$_1$ , and T$_2$ .

A 3 kg box is pushed on a surface with a force of F = 15 N. The coefficient of static friction, $\mu_s$ is 0.3, and the coefficient of kinetic friction, $\mu_k$ is 0.1.

A. Does the box move?

B. If it does move, calculate the acceleration of the box.

A M$_1$ = 5 kg box rests on a table and is connected to a second box of mass M$_2$ = 10 kg via a rope that hangs over a frictionless pulley as shown. The coefficient of friction, $\mu$ is 0.2, Use free body diagrams to answer the following:

B. What is the tension in the rope?

The large block m$_1$ is 10 kg, and the smaller block m$_2$ is 1 kg. The coefficient of kinetic friction is 0.1. Determine the acceleration of the system and the contact force between the blocks. The applied force, F is 30 N. Also draw a free body diagram for both blocks.

A box is being pulled with force Fa= 40 N at an angle θ= 30 degrees. There is a frictional force opposing the sliding of the box with force Ff= 10 N. Draw a free body diagram to help answer the following questions. (use gravity at 10m/s2 to simplify the numbers)

A 1.2 kg mass, m, is swinging on a string pendulum of length 80 cm (the string has negligible mass). As shown in the figure below, when $\theta$ is 10 degrees the velocity of the mass is 0.6 m/s. Find the tension in the string and the acceleration of the mass at this moment.

A student is about to be launched from a spring loaded canon. The student weighs 60 kg and the spring constant is 200 N/kg. Find the students velocity the moment he leaves the canon if the spring is compressed, x = 3 m. Also find the students velocity after the spring has decompressed to x = 2 m.

A nonlinear spring is compressed various distances x, and the force Frequired to compress it is measured for each distance. The data are shown in the table below.

A spherical non rotating planet has a radius R and a uniform density $ho$ throughout its volume. Suppose a narrow tunnel were drilled through the planet along one of its diameters as shown in the figure below, in which a small ball of mass m could move freely under the influence of gravity. Let r be the distance of the ball from the center of the planet. Suppose the ball is dropped into the tunnel from rest at the planet's surface.

F. Write an equation that could be used to calculate the time it takes the ball to move from point P to the center of the planet.

A 2kg car is traveling east at 3 m/s and a 4kg car is traveling west at 6 m/s. Assume the cars collide and stick together. Find the direction and velocity of the cars after they collide.

A champagne bottle of mass 90 g has a 2 g cork in it. The pressure built up in the bottle causes the cork to shoot out, as shown below. If after the explosion, the bottle is moving directly to the left at 4 m/s, what is the velocity of the cork?

A crash test car of mass 1,000 kg moving at a constant speed of 12 m/s collides completely inelastically with an object of mass M at time t = 0. The ojbect was initally at rest. The speed v in m/s of the car object system after the collision is given as a function of time t in seconds by the expression

$v = \frac{8}{1 + 5t}$

A. Calculate the mass M of the object

B. Assuming an initial position of x = 0, determine an expression for the position of the car object system after the collision as a function of time t.

C. Determine an expression for the resisting force on the car object system after the collision as a function of time t.

D. Determine the impulse delivered to the car object system from t = 0 to t = 2.0 s.

A flywheel turns through 40 rev as it slows from an angular speed of 1.5 rad/s to stop.

A. Assuming constant angular acceleration find the time for it to come to rest.

B. What is its angular acceleration?

C. How much time is required for it to complete its first 20 of the 40 revolutions?

An explorer plans a mission to place a satellite into a circular orbit around the planet Jupiter, which has a mass of M1= 1.90 x 1027kg and radius R1= 7.14 x 107m. A. If the radius of the planned orbit is R, use Newton’s laws to show each of the following.

The orbital speed of the planned satellite is give by v= $\sqrt{\frac{GM_1}{R}}$

The period of the orbit is given by T= $\sqrt{\frac{4\pi^2R^3}{GM_1}}$

B. The explorer wants the satellite’s orbit to be synchronized with Jupiter’s rotation. This requires an equatorial orbit whose period equals Jupiter’s rotation period of 9 hr 51 min = 3.55 x 105s. Determine the required orbital radius in meters. C. Suppose that the injection of the satellite into orbit is less than perfect. For an injection velocity that differs form the desired value in each of the following ways, sketch the resulting orbit on the figure. ( J is the center of Jupiter, the dashed circle is the desired orbit, and Pis the injection point.) Also, describe the resulting orbit qualitatively but specifically

When the satellite is at the desired altitude over the equator, its velocity vector has the correct direction, but the speed is slightly faster than the correct speed for a circular orbit of that radius.

When the satellite is at the desired altitude over the equation, its velocity vector has the correct direction but the speed is slightly slower than the correct speed for a circular orbit of that radius.

An oscillator consists of a block of mass 0.500 kg connected to a spring. When set into oscillation with amplitude 35.0 cm, the oscillator repeates its motion every 0.500 s. Find the:

A. period

B. frequency

C. angular frequency

D. spring constant

E. maximum speed

F. magnitude of maximum force on the block from the spring