B. Variable Force Supplied by Gravity You can find the value of the cart’s accel
ID: 1336944 • Letter: B
Question
B. Variable Force Supplied by Gravity
You can find the value of the cart’s acceleration down the ramp, a, by considering the forces acting on it as it moves. In Figure 6.3, the force of gravity (the cart’s weight mg) acts vertically downward. The component of the cart’s weight parallel to the ramp is mg sin ?, and the component perpendicular to the ramp is mg cos ?. The ramp pushes up on the cart with a normal force FN that is equal and opposite to mg cos ?, so the net force on the cart in that direction is zero. The cart therefore has no acceleration perpendicular to the ramp.
The cart’s acceleration parallel to the ramp, a, is the ratio of the parallel force mg sin ? to the mass m, or
a= gsin?
This acceleration will be directed down the ramp, no matter which direction the cart is moving. Because the cart’s velocity is proportional to the time (v = vo + at), a graph of velocity vs. time will be linear. The slope of the graph will be positive for motion down the ramp (v and a have the same sign) and will be negative for motion up the ramp (v and a have opposite signs), and the value of the slope will be equal to the cart’s acceleration. Because the cart’s acceleration is constant, a graph of a vs. t will be linear and horizontal, and the value of a will be the position of the horizontal line on the ordinate scale. The motion of the cart (its change in position with time) can be measured directly with a motion sensor. In Part B, what would be the shape of a graph of a vs. theta for motion on the inclined ramp? Why would the graph appear this way?
Preview File Edit View Go Tools Window Help Mon 12:56 PM a PHYS 2425 Exp 06 Manual.pdf (page 6 of 10) Q Search 78 tips, and much ad, iOS cose Share is Figure 6.3: Forces on block on a ramp 12Explanation / Answer
here theta is constant so sin is also constant. acceleration of block parallel to the ramp is gsin. where g is the acceleration due to gravity.
so value of acceleration is constant.
shape of a graph of a vs. theta for motion on the inclined ramp is straight line and parallel to line of theta.
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