Find the acceleration of a box being pulled with an applied force of 320.0N at an angle of 30° from the horizontal. The µk between the floor and the box is 0.30
mass of the box?
80 kg
To find the acceleration of the box, we need to consider the forces acting on the box. There are two main forces to consider: the applied force and the force of friction.
1. Resolve the applied force into its horizontal and vertical components:
- F_horizontal = F_applied * cos(theta) = 320.0 N * cos(30°) = 320.0 N * 0.866 = 277.12 N
- F_vertical = F_applied * sin(theta) = 320.0 N * sin(30°) = 320.0 N * 0.5 = 160.0 N
2. Determine the force of friction (F_friction) using the coefficient of kinetic friction (µk) and the normal force (F_normal).
- F_normal = m * g, where m is the mass of the box and g is the acceleration due to gravity (~9.8 m/s^2).
Let's assume the mass of the box is 10 kg.
F_normal = 10 kg * 9.8 m/s^2 = 98 N
- F_friction = µk * F_normal = 0.30 * 98 N = 29.4 N
3. Calculate the net force acting on the box in the horizontal direction:
- F_net_horizontal = F_horizontal - F_friction = 277.12 N - 29.4 N = 247.72 N
4. Use Newton's second law of motion to find the acceleration of the box:
- F_net_horizontal = m * a, where m is the mass of the box and a is its acceleration.
- a = F_net_horizontal / m = 247.72 N / 10 kg = 24.772 m/s^2
Therefore, the acceleration of the box being pulled with an applied force of 320.0 N at an angle of 30° from the horizontal, with a coefficient of kinetic friction of 0.30, is approximately 24.772 m/s^2.
To find the acceleration of the box being pulled, we need to consider the forces acting on the box. The horizontal component of the applied force will contribute to the acceleration, while the vertical component and the force of friction will counteract it.
1. Start by calculating the horizontal component of the applied force:
Horizontal component = Applied force × cos(angle)
Horizontal component = 320.0N × cos(30°)
Horizontal component = 320.0N × 0.866
Horizontal component ≈ 277.1N
2. Next, calculate the force of friction using the coefficient of kinetic friction (µk) and the normal force. The normal force is equal to the weight of the box, which is given by the equation:
Normal force = Mass × gravitational acceleration
Normal force = m × g
3. Assuming the mass of the box is m kg, and the gravitational acceleration is approximately 9.8 m/s^2, we can calculate the normal force:
Normal force = m × 9.8N/kg
4. Once we have the normal force, we can find the force of friction:
Force of friction = µk × Normal force
Force of friction = 0.30 × Normal force
5. The force of friction acts in the opposite direction of the applied force, so it has a negative sign.
6. Finally, we can find the net force acting on the box:
Net force = Horizontal component - Force of friction
7. Since acceleration is equal to the net force divided by the mass of the box (a = Fnet/m), we can calculate it:
Acceleration = Net force / m
By following these steps, you can calculate the acceleration of the box being pulled with the given information.