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# Help with this Mechanics question i don't know where to start. watch

1. A body of mass m kg is projected from a point A up the line of greatest slope of a plane inclined at 20° to the horizontal, as shown. The initial speed of the body is 10 ms-1.
(a) Assuming that the plane is smooth, find
(i) the acceleration of the body
(ii) the distance it travels up the plane before coming instantaneously to rest.

In fact the plane is rough. The coefficient of friction between the body and the plane is mew. The body comes to rest after 9 m.
(b) Calculate the value of mew. (5)
(c) Show that the body slides back down the plane, arriving at A with
speed 4.55 ms-1.
2. (Original post by TheBrownGuy)
A body of mass m kg is projected from a point A up the line of greatest slope of a plane inclined at 20° to the horizontal, as shown. The initial speed of the bodty is 10 ms-1.
(a) Assuming that the plane is smooth, find
(i) the acceleration of the body
(ii) the distance it travels up the plane before coming instantaneously to rest.

In fact the plane is rough. The coefficient of friction between the body and the plane is mew. The body comes to rest after 9 m.
(b) Calculate the value of mew. (5)
(c) Show that the body slides back down the plane, arriving at A with
speed 4.55 ms-1.

Start by drawing a diagram:

The masses acceleration up the slope is limited by the component of its weight acting down the slope. You can work out what this component is.
As the mass is projected, this is the only force acting on the mass.
With the information in the diagram, you can work out a formula for the component of the masses weight acting down the slope and use it in f = ma to get its negative acceleration/deceleration up the slope.
When you have this, you can find the distance using a simple SUVAT equation.

S = ? U = 10 V = 0 a = (you'll find this out)

For the next part of the question where you need to consider friction, you begin by finding out the masses acceleration using the information given,Then resolve the forces on the particle acting into, and parallel to the slope:
Attachment 474193
With this, you can write equations linking the forces acting on the particle to its acceleration, and the reaction force from the slope to the component of the masses weight acting into the slope.
Finally, just use the fact that F = R(mu) to find your co-efficient of friction. Hopefully this helps

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Updated: October 31, 2015
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