the tension in a string from which a 6.5 kg box is suspended in an elevator is equal to 52 N. what would be the magnitude of acceleration of the elevator if acceleration of gravity is 9.8 m/s?? would the direction be downward or upward??
To determine the magnitude of the acceleration of the elevator and its direction, you can use Newton's second law of motion. The tension in the string is equal to the force exerted on the box.
1. Write down the given information:
- Mass of the box (m) = 6.5 kg
- Tension in the string (T) = 52 N
- Acceleration due to gravity (g) = 9.8 m/s²
2. Identify the forces acting on the box:
- The force due to gravity acting on the box is equal to its weight: Fg = m * g
- The tension in the string is equal to the force exerted upwards: Fup = T
- The force acting on the box in the direction of acceleration is unknown: Facc
3. Apply Newton's second law (F = ma) in the vertical direction:
ΣFup - ΣFg - ΣFacc = ma
T - Fg - Facc = m * a
4. Substitute the known values:
52 N - (6.5 kg * 9.8 m/s²) - Facc = 6.5 kg * a
Note: We subtract the force due to gravity as it acts downwards.
5. Solve the equation for the unknown force (Facc):
Facc = 52 N - (6.5 kg * 9.8 m/s²)
Facc = 52 N - 63.7 N
Facc = -11.7 N
The negative sign indicates that the force is downward, opposing the tension.
6. Substitute the calculated force (Facc) into the equation:
-11.7 N = 6.5 kg * a
7. Solve for the magnitude of acceleration (a):
a = (-11.7 N) / (6.5 kg)
a ≈ -1.8 m/s²
The magnitude of the acceleration is approximately 1.8 m/s².
Since the acceleration is negative, it indicates that the elevator is moving downward.