91影视

$FIGURECP7.58$shows three hanging masses connected by massless strings over two massless, frictionless pulleys.

a. Find the acceleration constraint for this system. It is a single equation relatinglocalid="1649865348893" $a_{1y},a_{2y},and{a}_{3y}.$Hint:$y_A$isn鈥檛 constant.

b. Find an expression for the tension in string $A.$Hint: You should be able to write four second-law equations. These, plus the acceleration constraint, are five equations in five unknowns.

c. Suppose:$m_1=2.5kg,m_2=1.5kg,and{m}_3=4.0kg.$Find the acceleration of each.

d. The $4.0kg$mass would appear to be in equilibrium. Explain why it accelerates.

a. How much force does an $80kg$astronaut exert on his chair while sitting at rest on the launch pad?

b. How much force does the astronaut exert on his chair while accelerating straight up at $10m/s^2?$

A mosquito collides head-on with a car traveling $60mph.$Is the magnitude of the mosquito鈥檚 acceleration larger than, smaller than, or equal to the magnitude of the car鈥檚 acceleration? Explain.

A small car is pushing a large truck. They are speeding up. Is the force of the truck on the car larger than, smaller than, or equal to the force of the car on the truck?

Block B in the figure rests on a surface for which the static and kinetic coefficients of friction are $0.60$and $0.40$respectively. The ropes are massless.

What is the maximum mass of block A for which the system remains in equilibrium?

A very smart $3$-year-old child is given a wagon for her birthday. She refuses to use it. 鈥淎fter all,鈥� she says, 鈥淣ewton鈥檚 third law says that no matter how hard I pull, the wagon will exert an equal but opposite force on me. So I will never be able to get it to move forward.鈥� What would you say to her in reply?

A $1000kg$car pushes a $2000kg$truck that has a dead battery. When the driver steps on the accelerator, the drive wheels of the car push against the ground with a force of $4500N$. Rolling friction can be neglected.

a. What is the magnitude of the force of the car on the truck?

b. What is the magnitude of the force of the truck on the car?

Blocks with masses of $1kg,2kg\text{and}3kg$are lined up in a row on a frictionless table. All three are pushed forward by a $12N$force applied to the $1kg$block.

a. How much force does the $2kg$block exert on the $3kg$block?

b. How much force does the $2kg$block exert on the$1kg$block?

Teams red and blue are having a tug-of-war. According to Newton鈥檚 third law, the force with which the red team pulls on the blue team exactly equals the force with which the blue team pulls on the red team. How can one team ever win? Explain