A block is given n intial speed of 3.0 s^-1 m up the 22.0 degree plane
(a) How far up the plane will it go?
(b) How mcuh time elapses before it returns to its starting point?
Assume Mu k = 0.17
for (a)
a = - (Mu k g cos theta + g sin theta)
I got - 5.23 s^-1 m
for finding distance
x = (2a)^-1 (V^2 - Vo^2)
I got .87 m
ok in my book it gives me the answers in centimeters but still got right 87 cm for the time it gives me 1.5 s don't know how to get the time
t = a^-1 (V - Vo)
multiplied by two for time back
t = 1.15 s
don't know what to do
thanks
The average speed going up is 3/2 or 1.5m/s, so time up is .87/1.5 sec
Now going down, it has .87*sin22 height, so it willhave some vfinal at the bottom
1/2 m vf^2=mg (.87sin22)-.87*mgCos22
which means final KE=initial PE-friction
solve for vf, then avg velocity down is 1/2 vf, and then solve for time down, and add to time up.
To find the distance the block will go up the plane, you correctly calculated the acceleration using the formula:
a = -(μk * g * cos(theta) + g * sin(theta))
where μk is the coefficient of kinetic friction, g is the acceleration due to gravity, and theta is the angle of the plane. Plugging in the given values, we get:
a = -(0.17 * 9.8 * cos(22) + 9.8 * sin(22)) = -5.23 m/s^2
To find the distance traveled, you can use the kinematic equation:
x = (V^2 - Vo^2) / (2 * a)
where V is the final velocity, and Vo is the initial velocity (in this case, 0 since the block comes to rest at its maximum height). Plugging in the values, we get:
x = (0 - (3.0)^2) / (2 * (-5.23)) = 0.87 m
So the block will go 0.87 meters up the plane.
Now, to find the time it takes for the block to return to its starting point, we can use the fact that the time taken to go up the plane will be the same as the time taken to come back down. We can find the time it takes to go up the plane using the formula:
t = (V - Vo) / a
Plugging in the values, we get:
t = (0 - 3.0) / (-5.23) = 0.5733 s
Since the time taken to go up the plane is the same as the time taken to come back down, the total time will be twice the time calculated above:
t = 2 * 0.5733 = 1.15 s
So the time it takes for the block to return to its starting point is 1.15 seconds.