Question

What is the horizontal acceleration of a block of mass 10 Kg, if it is pulled to the right with a force of 19 N is applied at an angle of 21º (measured counterclockwise from the +x axis).

a) 2 m/s^2
b) 5 m/s^2
c) 8 m/s^2
d) 10 m/s^2

Answer 1

The block's horizontal acceleration is found by calculating the horizontal component of the applied force using the cosine of the angle, then applying Newton's second law. The calculation yields an acceleration of approximately 1.773 m/s², which is rounded to 2 m/s², matching option a).

Step-by-step explanation:

To find the horizontal acceleration of the block, we must start by identifying the horizontal component of the applied force. Since the force of 19 N is applied at an angle of 21° above the horizontal, we use the cosine function to find the horizontal component (Fx) of the force:

Fx = F × cos(θ) = 19 N × cos(21°) = 19 N × 0.9336 = 17.7284 N

Next, we apply Newton's second law, F = ma, where F is the net force, m is the mass, and a is the acceleration. Here, the net force is the horizontal component of the applied force because we're ignoring other forces like friction and air resistance:

a = Fx / m = 17.7284 N / 10 kg = 1.773 m/s²

Therefore, the horizontal acceleration of the block is approximately 1.773 m/s², which, when rounded to the nearest whole number, gives us 2 m/s². This corresponds to option a) 2 m/s².