A conical pendulum is formed by attaching a ball of mass \( m \) to a string of length \( \ell \), then allowing the ball to move in a horizontal circle of radius \( r \). The following figure shows that the string traces out the surface of a cone, hence the name.
A 0.2 kg object is attached to a horizontal spring undergoes SHM with the total energy of 0.4 J. The kinetic energy as a function of position presented by the graph.
An object is released from rest near the surface of a planet. The velocity of the object as a function of time is expressed in the following equation. \( v_y = (-3) \, \text{m/s}^2 \, t \) All frictional forces are considered to be negligible. What distance does the object fall \( 10 \) \( \text{s} \) after it is released from rest?
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 car can decelerate at \( -3.80 \, \text{m/s}^2 \) without skidding when coming to rest on a level road. What would its deceleration be if the road is inclined at \( 9.3^\circ \) and the car moves uphill? Assume the same static friction coefficient.
A person pulls a rope with a force \( F \) at an angle of \( 60^\circ \) to the horizontal. The rope is connected to a load over a frictionless pulley as shown in the diagram. The load is stationary. Which of the following is correct about the weight of the load and the net force exerted on the pulley by the rope?
The moment of inertia of a solid cylinder about its axis is given by \( 0.5MR^2 \). If this cylinder rolls without slipping, the ratio of its rotational kinetic energy to its translational kinetic energy is
Why do raindrops fall with constant speed during the later stages of their descent?
A ball is attached to the end of a string. It is swung in a vertical circle of radius \( 2.5 \) \( \text{m} \). What is the minimum velocity that the ball must have to make it around the circle?
Divers in Acapulco jump from a cliff that is \( 36 \, \text{m} \) above the water with an initial vertical velocity of \( 2 \, \text{m/s} \).
A delivery truck is traveling north. It then turns along a leftward circular curve. This the packages in the truck to slide to the RIGHT. Which of the following is true of the net force on the packages as they are sliding?
Two students push a \(1750\, \mathrm{kg}\) car with a force of \(758\, \mathrm{N}\) along a perfectly level road at a constant velocity of \(4.00\, \mathrm{m/s}\). Find the force of friction.
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