In which of the following is the rate of change of the particle’s momentum zero?
A rocket of mass m is launched with kinetic energy K0, from the surface of the Earth. How much less kinetic energy does the rocket have at an altitude of two Earth radii in terms of the gravitational constant, G; the mass of the Earth, mE ; the radius of the Earth, RE ; and the mass of the rocket?
A driver is driving at \( 40 \, \text{m/s} \) when the light turns red in front of her. It takes the driver \( 0.9 \, \text{s} \) to react and hit the brakes. After this, the car slows with an acceleration of \( 3.5 \, \text{m/s}^2 \). What is the total distance traveled by the car?
A meter stick of mass [katex] .2 [/katex] kg is pivoted at one end and supported horizontally. A force of [katex] 3 [/katex] N downwards is applied to the free end, perpendicular to the length of the meter stick. What is the net torque about the pivot point?
A wheel of radius R and negligible mass is mounted on a horizontal frictionless axle so that the wheel is in a vertical plane. Three small objects having masses [katex]m[/katex], [katex]M[/katex], and [katex]2M[/katex], respectively, are mounted on the rim of the wheel, as shown above. If the system is in static equilibrium, what is the value of [katex]m[/katex] in terms of [katex]M[/katex] ?
A spring launches a 4 kg block across a frictionless horizontal surface. The block then ascends a 30° incline with a kinetic friction coefficient of 0.25, stopping after 55 m on the incline. If the spring constant is 800 N/m, find the initial compression of the spring. Disregard friction while in contact with the spring.
In 2014, the European Space Agency placed a satellite in orbit around comet 67P/Churyumov-Gerasimenko and then landed a probe on the surface. The actual orbit was elliptical, but we can approximate it as a 50 km diameter circular orbit with a period of 11 days.
A girl throws a stone from a bridge. Consider the following ways she might throw the stone. The speed of the stone as it leaves her hand is the same in each case.
Case A: Thrown straight up.
Case B: Thrown straight down.
Case C: Thrown out at an angle of 45° above horizontal.
Case D: Thrown straight out horizontally.
In which case will the speed of the stone be greatest when it hits the water below if there is no significant air resistance, assuming equal initial speeds?
Friction provides the force needed for a car to travel around a flat, circular race track. Answer the following:
Measurements made in 1910 indicate that the common flea is an impressive jumper, given its size. Assume that a flea’s initial speed is 2.1 m/s, and that it leaps at an angle of 21° with respect to the horizontal. The jump lasts 0.16 s.
An airplane with a speed of \( 97.5 \, \text{m/s} \) is climbing upward at an angle of \( 50.0^\circ \) with respect to the horizontal. When the plane’s altitude is \( 732 \, \text{m} \), the pilot releases a package.
A uniform ladder of length L and weight [katex] W = 50 N [/katex] rests against a smooth vertical wall. If the coefficient of static friction between the ladder and the ground is [katex] \mu = .4 [/katex].
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