Answer:
The tension in the string will increase by a factor of two, while the acceleration will not change.
Explanation:
To approach this problem, we begin by sketching the situation and creating free body diagrams for both masses involved. (Refer to the attached image)
Let’s first examine the free body diagram for the cart. Assuming there’s no friction between the cart and the horizontal surface, and focusing solely on horizontal forces, we can write the force balance as follows:
Given that tension is the only horizontal force on the cart, we state:
Next, consider the hanging mass, taking downward as the positive direction. Summing forces yields:
The two forces acting here are gravity and tension, so:
Combining the two equations results in:
Solving for acceleration gives:
This represents the acceleration for the original setup. What happens if both masses are doubled? Let’s analyze:
Factoring 2 out of the denominator produces:
Which simplifies to:
You can observe this matches the original acceleration, confirming it remains unchanged.
Regarding tension, by substituting the doubled masses into the initial force expression:
The initial tension was:
Therefore, doubling the masses causes the tension to double as well.
Response:
The horizontal span of Sosa is 276.526 ft or 84.28 meters.
Explanation:
As illustrated in the diagram, let point O denote Sosa's starting position. She travels 361 ft at a 50-degree angle relative to the horizontal.
sin 50 =
0.7660 = h / 361
h = 276.526 ft
h = 84.28 meters
The horizontal distance of Sosa is 276.526 ft or 84.28 meters.
Answer:
The air exiting from the hairdryer is moving at a speed of 10 m/s.
Explanation:
The thrust generated by the hairdryer enables it to maintain an elevation angled at 5° from vertical; thus, we derive from the force diagram
by substituting ,
into the equation and resolving for
we find:
This thrust is linked to the speed of air ejection through the equation
where signifies the rate of air ejection, which is known to be
and since ,
by inserting these values into equation (2), we obtain the value of as:
resulting in
which indicates the air velocity discharged from the hairdryer.
