A 4700kg truck carrying a 900 kg crate is traveling at 25m/sto right on straight

Question

A 4700kg truck carrying a 900 kg crate is traveling at 25m/sto right on straight, level highway. Driver applies brakesand truck slows down traveling 55 m in next 3.0 s. The cratedoesn't slide on back of truck a. Calculate magnitude of acceleration of truck, assuming itis constant b. Calculate minimum coefficient of friction between crate andtruck that prevents crate from sliding c. Indicate whether this friction is static orkinetic Assume bed or truck is frictionless but there is now a springof spring constant 9200 N/m attaching crate to truck. Truckis initally at rest. d. If truck and crate have same acceleration, calculateextension of spring as truck accelerates from rest to 25m/s in 10s At some later time the truck is moving at constant speed of25m/s and crate is in equilibrium Indicate whether theextension of spring is greater than, less than, or same as (d) whentruck is accelerating. Explain reasoning. A 4700kg truck carrying a 900 kg crate is traveling at 25m/sto right on straight, level highway. Driver applies brakesand truck slows down traveling 55 m in next 3.0 s. The cratedoesn't slide on back of truck a. Calculate magnitude of acceleration of truck, assuming itis constant b. Calculate minimum coefficient of friction between crate andtruck that prevents crate from sliding c. Indicate whether this friction is static orkinetic Assume bed or truck is frictionless but there is now a springof spring constant 9200 N/m attaching crate to truck. Truckis initally at rest. d. If truck and crate have same acceleration, calculateextension of spring as truck accelerates from rest to 25m/s in 10s At some later time the truck is moving at constant speed of25m/s and crate is in equilibrium Indicate whether theextension of spring is greater than, less than, or same as (d) whentruck is accelerating. Explain reasoning.

Explanation / Answer

      a.   secondequation of motionis   d   =   u *t   +   (1/2) * a *t2             d   =   distance,   u   =   initialvelocity,   a   =   acceleration,   t   =   time.             55   =   25* 3.0   +   0.5 * a * 3.02             a   =   -40 / 9.0   =   -4.44   m/s2             a   =   -40 / 9.0   =   -4.44   m/s2            -ve sign is due to the fact that truck is deaccelerated and it canbe discarded.    b.   Acceleration ofcrate   a   =   * g       4.44   =   * 9.8   =>   coefficient offriction      =   4.44/ 9.8   =   0.453    c.   Since crates do notmove, the friction is static.    d.   Acceleration oftruck   =   (25 - 0) /10   =   2.5 m/s2          Sincetruck and crate have same acceleration, force exerted bycrate   =   F   =   m* a          F   =   900*2.5   =   2250   N          Extensionproduced inspring   x   =   F /k,      k   =   springconstant   =   9200   N/m          extension   x   =   2250/9200   =   0.244   m   =   24.4   cm    e.   Since there is noacceleration ( constant speed), the crate will not exert any forceof the spring and hence the extension would be zero.          Sincetruck and crate have same acceleration, force exerted bycrate   =   F   =   m* a          F   =   900*2.5   =   2250   N          Extensionproduced inspring   x   =   F /k,      k   =   springconstant   =   9200   N/m          extension   x   =   2250/9200   =   0.244   m   =   24.4   cm    e.   Since there is noacceleration ( constant speed), the crate will not exert any forceof the spring and hence the extension would be zero.

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