n as the block sides down the ramp? Wahat s the etfe o fition on the magnitude o

Question

n as the block sides down the ramp? Wahat s the etfe o fition on the magnitude of acceleratio increases acceleraton decreases atceleration no efect What s the efed o friction on the speed as the block leaves tne ramp? increases speed ecreases speed What is the efect f tricton o cn the horizcntai distance (R) the block travels betore it hits the floor? ncreases FR decresses R ro ehect whst is the efest of frection on the time elapsed from release of the block unti the black hits the flcor? increasestme desreses ime no olect

Explanation / Answer

for a block of mass m on incline of angle theta, coefficnet of friction k

1. acceleraTION OF BLOCK BE a

then, mgsin(theta) - k*mgcos(theta) = ma

a = gsin(theta) - k*gcos(theta)

so increasing friction decreases accelertation down the ramp

2. as acceleration has decreased due to increeasing friction

the speed with which the block leaves the ramp also decreases with increasing friction

3. As final speed has decreased due to increasing friction,

final speed = v

2*a*L = v^2

v = sqroot(2*a*L) where L is length of the ramp

now if the ramp is at height h

then , h = vsin(theta)*t + 0.5gt^2

and horizontal distance covered before hitting hte ground = R

R = vcos(theta)t

h = vsin(theta)*R/vcos(theta) + 0.5g(R^2/v^2*cos^2(theta))

0.5g*R^2/v^2*cos^2(theta) + tan(theta)*R - h = 0

so R = v^2*cos^2(theta)(-tan(theta) + sqrot(tan^2(theta) + 2gh/v^2cos^2(theta) ))/g

so when v decreases, R increases

so increasing friction decreases final speed and increases horizontal distance travelled by the block before hitting the ground

4. t = R/vcos(theta)

increasing friction increases R and decreases v so time of flight increases

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