Exam 6: Conservation of Energy

A 3.00 kg pendulum bob on a string 2.00 m long is released with a velocity of 2.00 m/s when the support string makes an angle of 45.0 degrees with the vertical. What is the tension in the string at the highest point of its motion?

A 2.00 kg pendulum bob on a string 1.50 m long, is released with a velocity of 3.00 m/s when the support string makes an angle of 45.0 degrees with the vertical. What is the tension in the string at the bottom of the swing?

An asteroid of radius 2.1 km is observed to have an escape speed equal to a typical person's maximum jumping speed, 3.0 m/s. What is its mass?

A 6.00 kg box is pulled up an 8.00 m long incline (with friction) at an angle of 30.0 degrees by a force of 50.0 N parallel to the incline. The coefficient of kinetic friction is 0.100. The work done against friction is

A 2.00 kg pendulum bob on a string 1.50 m long, is released with a velocity of 2.00 m/s when the support string makes an angle of 30.0 degrees with the vertical. What is the speed of the bob at the bottom of the swing?

A horizontal force is applied to a 2.0 kg box. The box starts from rest, moves a horizontal distance of 12.0 meters, and obtains a velocity of 8.0 m/s. The change in the kinetic energy is

A comet is observed to pass 1.50 × 10⁸ m from the surface of the Sun. The Sun's radius is 6.96 × 10⁸ m. What is the speed of the comet at this point, if its speed when passing the Earth's orbit, 1.50 × 10¹¹ m from the Sun's center, is 25 km/s? (M_S = 1.989 × 10³⁰ kg.)

A 20.0 kg box slides down a 12.0 m long incline at an angle of 30.0 degrees with the horizontal. A force of 50.0 N is applied to the box to try to prevent it from sliding down the incline. The applied force makes an angle of 10.00 degrees to the incline and above the incline. If the incline has a coefficient of kinetic friction of 0.100, then the increase in the kinetic energy of the box is

A 2.00 kg pendulum bob on a string 1.50 m long is released with a velocity of 0.00 m/s when the support string makes an angle of 60.0 degrees with the vertical. What is the tension in the string at the bottom of the swing?

A spring-powered dart gun is unstretched and has a spring constant 10.0 N/m. The spring is compressed by 8.00 cm and a 5.00 gram projectile is placed in the gun. The kinetic energy of the projectile when it is shot from the gun is

A 20.0 kg box slides up a 12.0 m long incline at an angle of 30.0 degrees with the horizontal. A force of 150 N is applied to the box to pull it up the incline. The applied force makes an angle of 0.00 degrees to the incline. If the incline has a coefficient of kinetic friction of 0.100, then the increase in the kinetic energy of the box is

A 2.00 kg pendulum bob on a string 3.00 m long is released with a velocity of 1.00 m/s when the support string makes an angle of 30.0 degrees with the vertical. What is the tension in the string at the highest point of its motion?

A blob of clay of mass M is propelled upward from a spring that is initially compressed by an amount d. The spring constant is k. What is the ultimate height h above the unstretched spring's end that the clay will reach?

A 2000 kg car accelerates from rest to a velocity of 40 m/s in 5.0 seconds. The brakes are applied, and the car is brought to a stop (without sliding). The magnitude of the work done by the friction in the brakes is

A 5.00 gram bullet has a velocity of 300 m/s. It strikes a block of wood and penetrates to a depth of 2.00 cm. The average force of the block of wood on the bullet is

A spring-powered dart gun is unstretched and has a spring constant 150 N/m. The spring is compressed by 8.00 cm and a 5.00 gram projectile is placed in the gun. The maximum height of the projectile when it is shot at an angle of 30.0 degrees above the horizontal from the gun is

A 20.0 kg box slides down a 12.0 m long incline at an angle of 30.0 degrees with the horizontal. A force of 50.0 N is applied to the box in the upward direction to try to prevent it from sliding down the incline. The applied force makes an angle of 10.0 degrees to the incline. If the incline has no friction, then the increase in the kinetic energy of the box is

When the escape speed from the surface of a spherical object of mass M and radius R is equal to the speed of light, that radius is called the Schwarzschild radius for the given mass. What is the Schwarzschild radius of the Sun, whose mass is 2.0 × 10³⁰ kg? (i.e., if all the Sun's mass were compressed into a sphere of this radius, the escape speed from its surface would be the speed of light-it would become a black hole!)

In order to conserve fuel, you modify your car by removing 100 kg of excess weight. How much energy is saved each time you accelerate from 0 to 100 km/hr (62 mph)?

During a basketball game, a player shoots a ball from half-court. When the ball reaches a height of 4.5 m above the floor, it is moving at 5.0 m/s. Assuming the shot was perfectly made, it will pass through the rim of the basket, 3.05 m above the floor. How fast is the ball moving when it passes through the rim?