a block , mass .10 kg, slides from rest without friction down an inclined plane 2m long which makes an angle of 20 degrees with the horizontal.(a) WWhat force accelerates the block down the plane?(b)j What is the velocity of the block when it reaches the botton of the pplane? (c) How long does it take the block to slide down the plane?
To find the answers to these questions, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the product of its mass and acceleration (F = m * a).
(a) What force accelerates the block down the plane?
Since there is no friction, the only force acting on the block along the incline is its weight. The weight force can be calculated using the formula: F = m * g, where m is the mass of the block and g is the acceleration due to gravity (approximately 9.8 m/s²). So the force accelerating the block down the plane is F = 0.10 kg * 9.8 m/s² = 0.98 N.
(b) What is the velocity of the block when it reaches the bottom of the plane?
To find the velocity of the block, we can use the kinematic equation: v² = u² + 2as, where v is the final velocity, u is the initial velocity (which is zero since the block starts from rest), a is the acceleration, and s is the distance traveled.
The distance traveled, s, is given as 2 m, and the acceleration, a, is the force acting on the block divided by its mass (from part (a)). So a = F / m = 0.98 N / 0.10 kg = 9.8 m/s².
Using the equation v² = 0² + 2 * 9.8 m/s² * 2 m, we can solve for v:
v² = 39.2 m²/s²
v = √39.2 m/s
v ≈ 6.26 m/s
Therefore, the velocity of the block when it reaches the bottom of the plane is approximately 6.26 m/s.
(c) How long does it take the block to slide down the plane?
To find the time it takes for the block to slide down the plane, we can use the formula: t = √(2s / a), where t is the time, s is the distance traveled, and a is the acceleration.
Using the given values, t = √(2 * 2 m / 9.8 m/s²) = √(0.408) s ≈ 0.64 s.
So it takes approximately 0.64 seconds for the block to slide down the plane.