7. Friction, Inclines, Systems

A 4.0-kg box sits on a frictionless inclined plane that makes a 21° angle with the horizontal. It is held in place by a cord parallel to the plane. Calculate the tension in the cord.

(II) A block is given an initial speed of 5.2m/s up the 22.0° plane shown in Fig. 4–45. <IMAGE>

(b) How much time elapses before it returns to its starting point? Ignore friction.

A parent pulls his child in a wagon across a floor. The child and wagon have a combined mass of 35 kg. The wagon handle is inclined at 55° to the horizontal, and the child and wagon (whose wheels are nearly frictionless) are accelerating at 0.42m/s² . With what force is the parent pulling on the wagon handle?

In the design of a supermarket, there are to be several ramps connecting different parts of the store. Customers will have to push grocery carts up the ramps and it is desirable that this not be too difficult. The engineer has done a survey and found that almost no one complains if the force required is no more than 23 N. Ignoring friction, at what maximum angle θ should the ramps be built, assuming a full 25-kg cart?

A car starts rolling down a 1-in-4 hill (1-in-4 means that for each 4 m traveled along the road, the elevation change is 1 m). How fast is it going when it reaches the bottom after traveling 55 m?

(a) Ignore friction.

A city planner is working on the redesign of a hilly portion of a city. An important consideration is how steep the roads can be so that even low-powered cars can get up the hills without slowing down. A particular small car, with a mass of 920 kg, can accelerate on a level road from rest to 21m/s (75km/h) in 14.5 s. Using these data, calculate the maximum steepness of a hill.