Question39. Find the acceleration of the body of mass 5.0 kg shown below.
Studdy Solution
STEP 1
1. The body has a mass of 5.0 kg.
2. Forces acting on the body are 10.0 N to the right, 2.0 N to the left, and 4.0 N downward.
3. We need to find the net acceleration of the body.
4. We assume the surface is frictionless unless otherwise stated.
5. We assume the only forces acting are those described in the problem.
STEP 2
1. Calculate the net force in the horizontal direction.
2. Calculate the net force in the vertical direction.
3. Determine the net force vector.
4. Calculate the acceleration using Newton's second law.
STEP 3
Calculate the net force in the horizontal direction: - The forces acting horizontally are 10.0 N to the right and 2.0 N to the left. - Net horizontal force .
STEP 4
Calculate the net force in the vertical direction: - The only force acting vertically is 4.0 N downward. - Net vertical force .
STEP 5
Determine the net force vector: - The net force vector is composed of the horizontal and vertical components. - Use the Pythagorean theorem to find the magnitude of the net force: F_{\text{net}} = \sqrt{(F_{\text{horizontal}})^2 + (F_{\text{vertical}})^2} = \sqrt{(8.0 \, \text{N})^2 + (4.0 \, \text{N})^2} \] F_{\text{net}} = \sqrt{64 + 16} = \sqrt{80} \approx 8.94 \, \text{N} \]
STEP 6
Calculate the acceleration using Newton's second law:
- Newton's second law states , where is the net force, is the mass, and is the acceleration.
- Rearrange to solve for acceleration: .
- Substitute the known values: .
- Calculate the acceleration: .
The acceleration of the body is:
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