Physics Force Problem (Please help!)

Question

A boulder weighing 2.0x10^4 N is resting on a hillside with a slope of 37 degrees

a) what force tends to cause the boulder to slide down the hill?

b) If there is no friction on the surface, what is the acceleration

c) How fast is it traveling after 7 meters

Answer 1

(a) what force tends to cause the boulder to slide down the hill?

As answered previously, Fx (down the hillside) is Fg * sin(37 degrees) = 2.0x10^4 N * sin(37 degrees) = 2.0x10^4 N * 0.60...

Fx = 1.2x10^4 N (to 2 significant digits), this is the answer to part (a)

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(b) If there is no friction on the surface, what is the acceleration?

As answered previously, without friction, the net force is Fx = 1.2x10^4 N

since Fx = m*a,

a = Fx / m, we need to find out what m is to solve this...

Since Fg = m * g = m * 9.8 m/s^2, we can solve for m...

m = Fg / g

Plugging in the values will yield...

m = 2.0x10^4 N / 9.8 m/s^2 = 2.0x10^4 kg-m/s^2 / 9.8 m/s^2

m = 2.04x10^3 kg

m = 2.0x10^3 kg (to 2 significant digits)

Now we can find the acceleration...

a = Fx / m = 1.2x10^4 N / 2.0x10^3 kg

a = 1.2x10^4 kg-m/s^2 / 2.0x10^3 kg

a = 6.0 m/s^2 (down the hillside, to 2 significant digits), this is the answer to part (b)

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c) How fast is it traveling after 7 meters?

This classic question is answered using a formula you should write down until you know it backwards and forwards...

vf^2 - v0^2 = 2*a*deltax

In this case, v0 = 0 m/s, a = 6.0 m/s^2, delta is 7 m, giving us...

vf^2 = 2 * 6.0 m/s^2 * 7 m

vf^2 = 84 m/s^2

vf = sqrt(84 m/s^2)

vf = 9.17 m/s

vf = 9 m/s (down the hill, to 1 significant digit), this is the answer to part (c)

note: the answer has 1 sig fig here, because delta was listed as 7 m, not 7.0 m

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Answer 2

A boulder weighing 2.0x10^4 N is resting on a hillside with a slope of 37 degrees

a) what force tends to cause the boulder to slide down the hill?

b) If there is no friction on the surface, what is the acceleration

c) How fast is it traveling after 7 meters

Start by drawing a picture....

The weight (force of gravity) is straight down. We need two components: The "normal force", which is perpendicular to the slope, and the "tangential force" which is in line with the slope.

The normal force is important only if there is friction involved.

The tangential force is the weight times sin(37): Ft = 2 * 10⁴ N * 0.602 = 1.20 * 10⁴ N

Acceleration occurs only along the slope (or away from it). Use F = m*a, where F is Ft