Math / Algebra

QuestionAn 80.0 kg man stands on a scale inside an elevator. What is the weight in Newtons that the scale reads when the elevator is: a. At rest b. Moving upward at a constant speed of $5.00 \mathrm{~m} / \mathrm{s}$ c. Moving downward at a constant speed of $5.00 \mathrm{~m} / \mathrm{s}$ d. Moving with an upward acceleration of $3.00 \mathrm{~m} / \mathrm{s} / \mathrm{s}$ e. Moving with a downward acceleration of $4.00 \mathrm{~m} / \mathrm{s} / \mathrm{s}$

Studdy Solution

STEP 1

1. The man's mass is $80.0 \, \text{kg}$ .
2. The acceleration due to gravity $g$ is $9.81 \, \text{m/s}^2$ .
3. The scale measures the normal force exerted by the man on the scale.

STEP 2

1. Calculate the weight when the elevator is at rest.
2. Calculate the weight when the elevator is moving at constant speed (upward and downward).
3. Calculate the weight when the elevator is accelerating upward.
4. Calculate the weight when the elevator is accelerating downward.

STEP 3

When the elevator is at rest, the only force acting on the man is gravity. The scale reads the gravitational force (weight).
Weight at rest: $W = mg = 80.0 \, \text{kg} \times 9.81 \, \text{m/s}^2 = 784.8 \, \text{N}$

STEP 4

When moving at constant speed (either upward or downward), there is no net acceleration. The forces are balanced, so the scale reads the same as when at rest.
Weight at constant speed (upward or downward): $W = 784.8 \, \text{N}$

STEP 5

When accelerating upward, the net force is the sum of gravitational force and the force due to acceleration.
Net force when accelerating upward: $F_{\text{net}} = m(g + a) = 80.0 \, \text{kg} \times (9.81 \, \text{m/s}^2 + 3.00 \, \text{m/s}^2) = 1024.8 \, \text{N}$

STEP 6

When accelerating downward, the net force is the gravitational force minus the force due to acceleration.
Net force when accelerating downward: $F_{\text{net}} = m(g - a) = 80.0 \, \text{kg} \times (9.81 \, \text{m/s}^2 - 4.00 \, \text{m/s}^2) = 464.8 \, \text{N}$
The weights read by the scale are: a. At rest: $784.8 \, \text{N}$ b. Moving upward at constant speed: $784.8 \, \text{N}$ c. Moving downward at constant speed: $784.8 \, \text{N}$ d. Moving with upward acceleration: $1024.8 \, \text{N}$ e. Moving with downward acceleration: $464.8 \, \text{N}$

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Studdy Solution

STEP 1

1. The man's mass is $80.0 \, \text{kg}$ .
2. The acceleration due to gravity $g$ is $9.81 \, \text{m/s}^2$ .
3. The scale measures the normal force exerted by the man on the scale.

STEP 2

1. Calculate the weight when the elevator is at rest.
2. Calculate the weight when the elevator is moving at constant speed (upward and downward).
3. Calculate the weight when the elevator is accelerating upward.
4. Calculate the weight when the elevator is accelerating downward.

STEP 3

When the elevator is at rest, the only force acting on the man is gravity. The scale reads the gravitational force (weight).
Weight at rest: $W = mg = 80.0 \, \text{kg} \times 9.81 \, \text{m/s}^2 = 784.8 \, \text{N}$

STEP 4

When moving at constant speed (either upward or downward), there is no net acceleration. The forces are balanced, so the scale reads the same as when at rest.
Weight at constant speed (upward or downward): $W = 784.8 \, \text{N}$

STEP 5

When accelerating upward, the net force is the sum of gravitational force and the force due to acceleration.
Net force when accelerating upward: $F_{\text{net}} = m(g + a) = 80.0 \, \text{kg} \times (9.81 \, \text{m/s}^2 + 3.00 \, \text{m/s}^2) = 1024.8 \, \text{N}$

STEP 6

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Studdy Solution

STEP 1

1. The man's mass is 80.0 kg 80.0 \, \text{kg} 80.0kg.2. The acceleration due to gravity g g g is 9.81 m/s2 9.81 \, \text{m/s}^2 9.81m/s2.3. The scale measures the normal force exerted by the man on the scale.

STEP 2

1. Calculate the weight when the elevator is at rest.2. Calculate the weight when the elevator is moving at constant speed (upward and downward).3. Calculate the weight when the elevator is accelerating upward.4. Calculate the weight when the elevator is accelerating downward.

STEP 3

When the elevator is at rest, the only force acting on the man is gravity. The scale reads the gravitational force (weight).Weight at rest: W=mg=80.0 kg×9.81 m/s2=784.8 N W = mg = 80.0 \, \text{kg} \times 9.81 \, \text{m/s}^2 = 784.8 \, \text{N} W=mg=80.0kg×9.81m/s2=784.8N

STEP 4

When moving at constant speed (either upward or downward), there is no net acceleration. The forces are balanced, so the scale reads the same as when at rest.Weight at constant speed (upward or downward): W=784.8 N W = 784.8 \, \text{N} W=784.8N

STEP 5

STEP 6

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1. The man's mass is $80.0 \, \text{kg}$ .
2. The acceleration due to gravity $g$ is $9.81 \, \text{m/s}^2$ .
3. The scale measures the normal force exerted by the man on the scale.

1. Calculate the weight when the elevator is at rest.
2. Calculate the weight when the elevator is moving at constant speed (upward and downward).
3. Calculate the weight when the elevator is accelerating upward.
4. Calculate the weight when the elevator is accelerating downward.

When the elevator is at rest, the only force acting on the man is gravity. The scale reads the gravitational force (weight).
Weight at rest: $W = mg = 80.0 \, \text{kg} \times 9.81 \, \text{m/s}^2 = 784.8 \, \text{N}$

When moving at constant speed (either upward or downward), there is no net acceleration. The forces are balanced, so the scale reads the same as when at rest.
Weight at constant speed (upward or downward): $W = 784.8 \, \text{N}$