Question. If the rocket sled shown in the previous problem starts with only one rocket burning, what is the magnitude of this acceleration? Assume that the mass of the system is $2.10 \times 10^{3} \mathrm{~kg}$ , the thrust T is $2.40 \times 10^{4} \mathrm{~N}$ , and the force of friction opposing the motion is 650.0 N . (b) Why is the acceleration not onefourth of what it is with all rockets burning?

Studdy Solution

STEP 1

1. The mass of the system is $2.10 \times 10^{3} \, \text{kg}$ .
2. The thrust $T$ of one rocket is $2.40 \times 10^{4} \, \text{N}$ .
3. The force of friction opposing the motion is $650.0 \, \text{N}$ .
4. We need to calculate the acceleration with one rocket burning.
5. We need to explain why the acceleration is not one-fourth of the acceleration with all rockets burning.

STEP 2

1. Calculate the net force acting on the sled.
2. Use Newton's second law to find the acceleration.
3. Explain why the acceleration is not one-fourth of the acceleration with all rockets burning.

STEP 3

Calculate the net force acting on the sled by subtracting the force of friction from the thrust of the rocket.
$F_{\text{net}} = T - F_{\text{friction}} = 2.40 \times 10^{4} \, \text{N} - 650.0 \, \text{N}$

STEP 4

Compute the net force:
$F_{\text{net}} = 2.40 \times 10^{4} \, \text{N} - 650.0 \, \text{N} = 2.335 \times 10^{4} \, \text{N}$

STEP 5

Use Newton's second law to find the acceleration $a$ :
$a = \frac{F_{\text{net}}}{m} = \frac{2.335 \times 10^{4} \, \text{N}}{2.10 \times 10^{3} \, \text{kg}}$

STEP 6

Calculate the acceleration:
$a = \frac{2.335 \times 10^{4} \, \text{N}}{2.10 \times 10^{3} \, \text{kg}} \approx 11.12 \, \text{m/s}^2$

STEP 7

Explain why the acceleration is not one-fourth of the acceleration with all rockets burning:
The acceleration is not one-fourth of the acceleration with all rockets burning because the force of friction is a constant value that does not scale with the number of rockets. When all rockets are burning, the total thrust is significantly higher, but the friction remains the same. Thus, the net force and resulting acceleration do not scale linearly with the number of rockets.
The magnitude of the acceleration with one rocket burning is approximately $11.12 \, \text{m/s}^2$ .

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Studdy Solution

STEP 1

STEP 2

1. Calculate the net force acting on the sled.
2. Use Newton's second law to find the acceleration.
3. Explain why the acceleration is not one-fourth of the acceleration with all rockets burning.

STEP 3

Calculate the net force acting on the sled by subtracting the force of friction from the thrust of the rocket.
$F_{\text{net}} = T - F_{\text{friction}} = 2.40 \times 10^{4} \, \text{N} - 650.0 \, \text{N}$

STEP 4

Compute the net force:
$F_{\text{net}} = 2.40 \times 10^{4} \, \text{N} - 650.0 \, \text{N} = 2.335 \times 10^{4} \, \text{N}$

STEP 5

Use Newton's second law to find the acceleration $a$ :
$a = \frac{F_{\text{net}}}{m} = \frac{2.335 \times 10^{4} \, \text{N}}{2.10 \times 10^{3} \, \text{kg}}$

STEP 6

Calculate the acceleration:
$a = \frac{2.335 \times 10^{4} \, \text{N}}{2.10 \times 10^{3} \, \text{kg}} \approx 11.12 \, \text{m/s}^2$

STEP 7

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Studdy Solution

STEP 1

STEP 2

1. Calculate the net force acting on the sled.2. Use Newton's second law to find the acceleration.3. Explain why the acceleration is not one-fourth of the acceleration with all rockets burning.

STEP 3

Calculate the net force acting on the sled by subtracting the force of friction from the thrust of the rocket.Fnet=T−Ffriction=2.40×104 N−650.0 NF_{\text{net}} = T - F_{\text{friction}} = 2.40 \times 10^{4} \, \text{N} - 650.0 \, \text{N}Fnet​=T−Ffriction​=2.40×104N−650.0N

STEP 4

Compute the net force:Fnet=2.40×104 N−650.0 N=2.335×104 NF_{\text{net}} = 2.40 \times 10^{4} \, \text{N} - 650.0 \, \text{N} = 2.335 \times 10^{4} \, \text{N}Fnet​=2.40×104N−650.0N=2.335×104N

STEP 5

Use Newton's second law to find the acceleration a a a:a=Fnetm=2.335×104 N2.10×103 kga = \frac{F_{\text{net}}}{m} = \frac{2.335 \times 10^{4} \, \text{N}}{2.10 \times 10^{3} \, \text{kg}}a=mFnet​​=2.10×103kg2.335×104N​

STEP 6

Calculate the acceleration:a=2.335×104 N2.10×103 kg≈11.12 m/s2a = \frac{2.335 \times 10^{4} \, \text{N}}{2.10 \times 10^{3} \, \text{kg}} \approx 11.12 \, \text{m/s}^2a=2.10×103kg2.335×104N​≈11.12m/s2

STEP 7

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1. Calculate the net force acting on the sled.
2. Use Newton's second law to find the acceleration.
3. Explain why the acceleration is not one-fourth of the acceleration with all rockets burning.

Calculate the net force acting on the sled by subtracting the force of friction from the thrust of the rocket.
$F_{\text{net}} = T - F_{\text{friction}} = 2.40 \times 10^{4} \, \text{N} - 650.0 \, \text{N}$

Compute the net force:
$F_{\text{net}} = 2.40 \times 10^{4} \, \text{N} - 650.0 \, \text{N} = 2.335 \times 10^{4} \, \text{N}$

Use Newton's second law to find the acceleration $a$ :
$a = \frac{F_{\text{net}}}{m} = \frac{2.335 \times 10^{4} \, \text{N}}{2.10 \times 10^{3} \, \text{kg}}$

Calculate the acceleration:
$a = \frac{2.335 \times 10^{4} \, \text{N}}{2.10 \times 10^{3} \, \text{kg}} \approx 11.12 \, \text{m/s}^2$