The horizontal surface on which the block of
mass 5.2 kg slides is frictionless. The force of
64 N acts on the block in a horizontal direction
and the force of 128 N acts on the block at an
angle as shown below.
5.2 kg
128 N
60
◦
64 N
What is the magnitude of the resulting acceleration of the block? The acceleration of
gravity is 9.8 m/s
2
.
Answer in units of m/s
2
To find the magnitude of the resulting acceleration of the block, we need to resolve the forces acting on the block and use Newton's second law of motion, which states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.
Let's break down the forces into their horizontal and vertical components:
The 64 N force is already in the horizontal direction, so its horizontal component is 64 N.
The 128 N force is acting at an angle of 60 degrees. To find its horizontal component, we can multiply the force by the cosine of the angle:
Horizontal component = 128 N * cos(60°)
The mass of the block is given as 5.2 kg.
To find the resulting acceleration, we need to find the net force acting on the block. The net force is the vector sum of the individual forces.
The horizontal net force can be found by adding the horizontal components of the forces:
Net force in the x-direction = 64 N + 128 N * cos(60°)
Using Newton's second law, we can find the resulting acceleration:
Acceleration = Net force / mass
Substituting the values, we get:
Acceleration = (64 N + 128 N * cos(60°)) / 5.2 kg
Now, we can calculate the magnitude of the resulting acceleration:
Acceleration = (64 N + 128 N * cos(60°)) / 5.2 kg
Acceleration ≈ (64 N + 128 N * 0.5) / 5.2 kg
Acceleration ≈ (64 N + 64 N) / 5.2 kg
Acceleration ≈ 128 N / 5.2 kg
Acceleration ≈ 24.62 m/s²
So, the magnitude of the resulting acceleration of the block is approximately 24.62 m/s².