1D and 2D Kinematics
An object is thrown straight up at 30 m/s. How long until it returns to launch height?
6.12 s
Two masses of 4.0 kg and 6.0 kg hang on a massless pulley. What is the acceleration?
0.98 m/s2
A 2.0 kg block slides down a frictionless incline from height 4.0 m. What is its speed at the bottom?
5.96 m/s
A 1.2 kg object moves in a horizontal circle of radius 0.80 m at a constant speed of 4.0 m/s. Determine the centripetal acceleration of the object.
20.0 m/s², directed toward the center of the circle
A 2.0 kg cart moves to the right at 3.0 m/s and collides head-on with a stationary 1.0 kg cart on a frictionless track. The carts stick together. Determine the final velocity of the combined system.
2.0 m/s [R]
A projectile is launched at 20 m/s at 30 degrees. What is its maximum height?
5.10 m
A 5.0 kg block on a 30° incline is connected over a pulley to a hanging 3.0 kg mass.
What is the acceleration of the system?
0.98 m/s2
A 1.5 kg block slides down a 30° incline of length 6.0 m with kinetic friction coefficient 0.20. What is its speed at the bottom?
5.96 m/s
A satellite of mass 900 kg orbits Earth in a circular orbit of radius 7.0 * 106 m (measured from Earth’s center). Determine the magnitude of the gravitational force exerted on the satellite by Earth.
(Earth’s mass is 6.0 * 1024 kg.)
7.35 × 10³ N
A 0.50 kg cart moving to the right at 4.0 m/s collides elastically with a 1.0 kg cart initially at rest. Determine the velocity of the 0.50 kg cart after the collision.
1.33 m/s [L]
Position is given by x(t) = 2t3 - 6t.
What is the acceleration at t = 2 s?
24 m/s²
A 5.0 kg block on a 30° incline is connected over a pulley to a hanging 3.0 kg mass. The coefficient of kinetic friction is 0.2. What is the acceleration?
0.04 m/s2
A 3.0 kg block slides from height 5.0 m on a frictionless track and compresses a spring by 0.40 m. What is the spring constant?
9.19 * 102 N/m
A 2.0 × 10³ kg satellite moves in a circular orbit around Earth at a radius of 8.0 * 106 m. Determine the direction of the net force acting on the satellite and explain whether this force changes the satellite’s speed.
Toward the center of the Earth; the force changes the direction of velocity but not the speed
A 1.5 kg cart moving to the right at 6.0 m/s collides with a 2.5 kg cart moving to the left at 2.0 m/s. After the collision, the carts stick together. Determine the final velocity of the system.
1.0 m/s [R]
Two objects start from rest at the same point. Object A has acceleration a, object B has acceleration 3a. How long after A must B start so they arrive together?
0 s
Two blocks (2.0 kg hanging, 6.0 kg on a frictionless 30° incline) are connected by a string over a pulley.
What is the tension in the string?
25.5 N
A pendulum bob of mass 0.80 kg is released from height 1.25 m and compresses a spring by 0.20 m at the bottom. What is the spring constant?
4.90 * 102 N/m
A satellite moves in a circular orbit around a planet with constant speed. The satellite completes one full orbit in 2.0 hours. Determine the direction of the satellite’s velocity vector and the direction of its acceleration vector at any point in the orbit.
Velocity is tangent to the circular path; acceleration is directed radially inward toward the planet
A 0.020 kg bullet traveling to the right at 400 m/s embeds in a 1.98 kg block attached to a horizontal spring with spring constant 800 N/m. The surface is frictionless. After the collision, the block–bullet system compresses the spring and momentarily comes to rest. Determine the maximum compression of the spring.
0.20 m
A projectile’s range equals four times its maximum height. What is its launch angle?
45°
Two blocks are connected by a light, inextensible string that passes over a massless, frictionless pulley. One block of mass 4.0 kg rests on a 30° incline that has a coefficient of kinetic friction of 0.25, while the other block of mass 6.0 kg hangs vertically. A horizontal force of 12 N is applied to the block on the incline, directed up the incline. The system is released from rest. What is the magnitude of the acceleration if the system?
0.73 m/s2
A 2.0 kg block slides down a rough 30° incline from height 6.0 m, then compresses a spring by 0.30 m and stops. If the coefficient of kinetic friction is 0.25, what is the spring constant?
6.07 * 102 N/m
A satellite of mass 500 kg orbits a planet of mass 4.0 * 1024 kg in a circular orbit of radius 2.0 * 107 m. Using the gravitational force as the centripetal force, determine the magnitude of the satellite’s acceleration.
6.67 m/s²
A 0.80 kg pendulum bob is released from a height of 2.5 m and swings down, colliding inelastically with a 1.20 kg block at rest on a frictionless surface. The pendulum bob has a speed of 5.0 m/s immediately as it is released. After the collision, the bob and block move together. Determine the velocity immediately after the collision.
2.0 m/s [R]